Related papers: On Admissible States of Quantum Fourier Transform
The Hilbert space of a physical qubit typically features more than two energy levels. Using states outside the qubit subspace can provide advantages in quantum computation. To benefit from these advantages, individual states of the…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient…
Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity,…
With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of…
Quantum computers have the potential to solve important problems which are fundamentally intractable on a classical computer. The underlying physics of quantum computing platforms supports using multi-valued logic, which promises a boost in…
We consider the separability of various joint states of D-dimensional quantum systems, which we call "qudits." We derive two main results: (i) the separability condition for a two-qudit state that is a mixture of the maximally mixed state…
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on…
Compared with a qubit, a qutrit (i.e., three-level quantum system) has a larger Hilbert space and thus can be used to encode more information in quantum information processing and communication. Here, we propose a scheme to transfer an…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms…
In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take…
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference…
Although only two quantum states of a physical system are often used to encode quantum information in the form of qubits, many levels can in principle be used to obtain qudits and increase the information capacity of the system. To take…
Some explanations and implications of the underlying theory approach for quantum theories (QM or QFT) are discussed and suggested. This simple idea seems to have significantly nontrivial effects for our understanding of the quantum…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
A simple and flexible scheme for high-dimensional linear quantum operations on optical transverse spatial modes is demonstrated. The quantum Fourier transformation (QFT) and quantum state tomography (QST) via symmetric informationally…
We propose a quantum state transfer from an atomic qubit to a cat-like qubit by means of one degenerate Raman interaction and one Hadamard gate operation for coherent states. We show that the coefficients of the atomic qubit can be mapped…